Part 3

Perhaps as remarkable a discovery as any one of the preceding (and one which, like those, has been rediscovered and confirmed by later physicists; one which was the subject of dispute between Clausius, who proved its truth by the later methods which are now the source of his fame, and the physicists of his earlier days, who had obtained inaccurate measures of the specific heats of the gases;—values which were finally corrected by Regnault, thus proving Carnot and Clausius to be right—is thus stated by Carnot, and is italicized in his manuscript and book:

“La différence entre la chaleur spécifique sous pression constante et la chaleur spécifique sous volume constant est la même pour tous les gaz.”

He bases his conclusion upon the simplest of thermodynamic considerations. He says that the increase of volumes with the same differences of temperature are the same, according to Gay-Lussac and Dalton; and that, therefore, according to the laws of thermodynamics as he has demonstrated them, the heat absorbed with equal augmentations of volume being the same, the two specific heats are constant, and their difference as well. As will be seen on referring to the text, he bases upon this principle a determination of the specific heats of constant volume, taking as his values of the determined specific heats of constant pressure those of Delaroche and Bérard, making the constant difference 0.300, that of air at constant pressure being taken as the standard and as unity. The establishment of this point, in the face of the opposition, and apparently of the facts, of the best physicists of his time, was one of those circumstances which did so much to win for Clausius his great fame. How much greater credit, then, should be given Carnot, who not only anticipated the later physicists in this matter, but who must have enunciated his principle under far more serious discouragements and uncertainty!

It must be remembered, when reading Carnot, that all the “constants of nature” were, in his time, very inaccurately ascertained. It is only since the time of Regnault’s grand work that it has been the rule that such determinations have been published only when very exactly determined. No change has been attempted in Carnot’s figures, in any respect; as it would be far less satisfactory to read a paraphrased work, and the exact figures are now easily accessible to every one, and his computations may all be made, if desired, on the basis of modern data. Sir William Thomson has already performed this task in the paper appended.

Throughout the whole of this treatise, small as it is, we find distributed a singular number of these anticipations of modern thermodynamic principles. Studying the relation of heat-energy to work done, he concludes:

“La chute du calorique produit plus de puissance motrice dans les degrés inférieurs que dans les degrés supérieurs.”

We to-day admit that, since the one degree at a low temperature, and the corresponding quantity of heat, are larger fractions of the total temperature, and the total heat stored in the substance, than the one degree at a higher point on the scale of absolute temperature, this principle of Carnot has become obvious.

In the enunciation of the essential principles of efficiency of the heat-engine, we find the proofs of this same wonderful prescience. He asserts that, for best effect: “(1) The temperature of the working fluid must be raised to the highest degree possible, in order to secure a commensurate range of temperature; (2) The cooling must be carried to the lowest point on the scale that may be found practicable; (3) The passage of the fluid from the upper to the lower limit of temperature must be produced by expansion;” i.e., “it is necessary that the cooling of the gas shall occur spontaneously by its rarefaction;” which is simply his method of stating the now universally understood principle that, for highest efficiency, the expansion must be adiabatic, from a maximum to a minimum temperature. He goes on to explain these principles, and then says that the advantage of high-pressure engines lies “essentiellement dans la faculté de rendre utile une plus grande chute de calorique.” This principle, as a practical system of operation, had already, as he tells us, been enunciated by M. Clement, and had been practised, as we well know, since the days of its originator, Watt; but Carnot saw clearly the thermodynamic principle which underlies it, and as clearly states it, for the first time.

He sees clearly, too, the reasons for the attempts of Hornblower and of Woolf, premature as they proved and as he also sees, in the introduction of the compound engine, and even suggests that this idea might be still further developed by the use of a triple-expansion engine, a type which is to-day just coming into use, more than a half-century after Carnot’s date. He recognizes the advantages of the compound engine in better distribution of pressures and in distribution of the work of expansion, but does not, of course, perceive the then undiscovered limitation of the efficiency of the simple engine, due to “cylinder condensation,” which has finally led, perhaps more than any other circumstance, to its displacement so largely by the multi-cylinder machine. No one has more exactly and plainly stated the respective advantages to be claimed for air and the gases, used as working fluids in heat-engines, than does Carnot; nor does any one to-day better recognize the difficulties which lie in the path to success in that direction, in the necessity of finding a means of handling them at high temperatures and of securing high mean pressures.

His closing paragraph shows his extraordinary foresight, and the precision with which that wonderful intellect detected the practical elements of the problem which the engineer, from the days of Savery, of Newcomen, and of Watt has been called upon to study, and the importance of the work, which he began, in the development of a theory of the action, or of the operation, of the heat-engines, which should give effective assistance in the development of their improved forms:

“On ne doit pas se flatter de mettre jamais à profit, dans la pratique, toute la puissance des combustibles. Les tentatives que l’on ferait pour approcher ce résultat seraient même plus nuisibles qu’utiles, si elles faisaient négliger d’autres considérations importantes. L’économie du combustible n’est qu’une des conditions à remplir par les machines à feu; dans beaucoup de circonstances, elle n’est que secondaire: elle doit souvent céder le pas à la sûreté, à la solidité, à la durée de la machine, au peu de place qu’il faut lui faire occuper, au peu de frais de son établissement, etc. Savoir apprécier, dans chaque cas, à leur juste valeur, les considérations de convenance et d’économie qui peuvent se présenter; savoir discerner les plus importantes de celles qui sont seulement accessoires, les balancer toutes convenablement entre elles, afin de parvenir, par les moyens les plus faciles, au meilleur résultat: tel doit être le principal talent de l’homme appelé à diriger, à co-ordonner entre eux les travaux de ses semblables, à les faire concourir vers un but utile de quelque genre qu’il soit.”

Such was the work and such the character of this wonderful man. Those whose desire to follow more closely and to witness the process of development of the work of which this initial paper of Carnot was the introductory, should study the contribution of Sir William Thomson to this development, as published in 1849,—a paper which constitutes that physicist the virtual discoverer of Carnot and the godfather of the man and his thoughts. This paper constitutes the final chapter of this little book.

From that time the additional progress so rapidly made in the new science was as inevitable as the development of a gold-field, once the precious metal has been found in paying quantities in the hitherto unvisited cañons and gorges of a distant and unexplored mountain-range. But great as is the work since done, and great as have been the discoveries and the discoverers of later years, none claims our gratitude and compels our respect in greater degree than does the original discoverer—

SADI CARNOT.

II. LIFE OF SADI CARNOT.

BY M. H. CARNOT.

As the life of Sadi Carnot was not marked by any notable event, his biography would have occupied only a few lines; but a scientific work by him, after remaining long in obscurity, brought again to light many years after his death, has caused his name to be placed among those of great inventors. In regard to his person, his mind, his character, nothing whatever has been known. Since there remains a witness of his private life—the sole witness, has he not a duty to fulfil? Ought he not to satisfy the natural and legitimate interest which attaches to any man whose work has deserved a portion of glory?

Nicolas-Léonard-Sadi Carnot was born June 1, 1796, in the smaller Luxembourg. This was that part of the palace where our father then dwelt as a member of the Directory. Our father had a predilection for the name of Sadi, which recalled to his mind ideas of wisdom and poetry. His firstborn had borne this name, and despite the fate of this poor child, who lived but a few months, he called the second also Sadi, in memory of the celebrated Persian poet and moralist.

Scarcely a year had passed when the proscription, which included the Director, obliged him to give up his life, or at least his liberty, to the conspirators of fructidor. Our mother carried her son far from the palace in which violation of law had just triumphed. She fled to St. Omer, with her family, while her husband was exiled to Switzerland, then to Germany.

Our mother often said to me, “Thy brother was born in the midst of the cares and agitations of grandeur, thou in the calm of an obscure retreat. Your constitutions show this difference of origin.”

My brother in fact was of delicate constitution. He increased his strength later, by means of varied and judicious bodily exercises. He was of medium size, endowed with extreme sensibility and at the same time with extreme energy, more than reserved, almost rude, but singularly courageous on occasion. When he felt himself to be contending against injustice, nothing could restrain him. The following is an anecdote in illustration.

The Directory had given place to the Consulate. Carnot, after two years of exile, returned to his country and was appointed Minister of War. Bonaparte at the same time was still in favor with the republicans. He remembered that Carnot had assisted him in the beginning of his military career, and he resumed the intimate relation which had existed between them during the Directory. When the minister went to Malmaison to work with the First Consul, he often took with him his son, then about four years old, to stay with Madame Bonaparte, who was greatly attached to him.

She was one day with some other ladies in a small boat on a pond, the ladies rowing the boat themselves, when Bonaparte, unexpectedly appearing, amused himself by picking up stones and throwing them near the boat, spattering water on the fresh toilets of the rowers. The ladies dared not manifest their displeasure, but the little Sadi, after having looked on at the affair for some time, suddenly placed himself boldly before the conqueror of Marengo, and threatening him with his fist, he cried “Beast of a First Consul, will you stop tormenting those ladies!”

Bonaparte, at this unexpected attack, stopped and looked in astonishment at the child. Then he was seized with a fit of laughter in which all the spectators of the scene joined.

At another time, when the minister, wishing to return to Paris, sought his son, who had been left with Madame Bonaparte, it was discovered that he had run away. They found him a long way off, in a mill, the mechanism of which he was trying to understand. This desire had been in the child’s mind for days, and the honest miller, not knowing who he was, was kindly answering all his questions. Curiosity, especially in regard to mechanics and physics, was one of the essential traits of Sadi’s mind.

On account of this disposition so early manifested, Carnot did not hesitate to give a scientific direction to the studies of his son. He was able to undertake this task himself when the monarchical tendencies of the new government had determined him to retire. For a few months only Sadi followed the course of M. Bourdon at the Charlemagne Lycée to prepare himself for the Polytechnic School.

The pupil made rapid progress. He was just sixteen years old when he was admitted to the school, the twenty-fourth on the list. This was in 1812. The following year he left it, first in artillery. But he was considered too young for the school of Metz, and he continued his studies at Paris for a year. To this circumstance is due the fact that he took part in March, 1814, in the military exploits of Vincennes, and not of the butte Chaumont, as almost all the historians of the siege of Paris declared. M. Chasles, one of Sadi’s school-fellows, took pains to rectify this error at a séance of the Institute in 1869.

If the pupils of the Polytechnic School did not earlier enter into the campaign, it was not because they had not asked to do so. I find in my brother’s papers the copy of an address to the Emperor, signed by them December 29, 1813: